Biometric authentication system

ABSTRACT

A 1:N identification system having high convenience and safety is to be provided. An authentication client includes at least one biometric information input sensor and a feature extraction function. A database includes an enrollee ID and registered templates of biometric information of at least one kind every enrollee and includes a score table. An authentication server includes a prior probability setting function, a 1:N fast matching function for successively matching the feature with the registered templates of the enrollees and discontinuing matching processing when the number of times of matching has exceeded a predetermined threshold, a delta score calculation function for calculating a delta score by using a score obtained by the 1:N fast matching and using the score table, a posterior probability calculation function for calculating posterior probabilities respectively of the enrollees on the basis of the score and the delta score, and an authentication object user identification function.

INCORPORATION BY REFERENCE

The present application claims priority from Japanese applicationJP2010-013747 filed on Jan. 26, 2010, the content of which is herebyincorporated by reference into this application.

BACKGROUND

The present invention relates to a method and system for authenticatingan individual by using a biometrical feature that the individual has.

The biometric authentication is known as an authentication techniquehaving an advantage that there is no forgetting and forgery is difficultas compared with authentication based on a password or a Smart card. Inthe biometric authentication, biometric information is acquired from auser (hereafter referred to as enrollee) and information called featureis extracted from the biometric information and registered, at time ofregistration. This registration information is called registeredtemplate. At time of authentication, a feature extracted from a user(hereafter referred to as authentication object user) is matched withthe template, and authentication is conducted by using an obtainedsimilarity which represents how alike two feature are or an obtainedscore representing a distance which represents how different two featureare (hereafter referred to as score).

Biometric authentication in which the authentication object user ismatched with each of N enrollees (hereafter referred to as 1:N matching)to identify which of the enrollees is the same person as theauthentication object user is called 1:N biometric identification. It atthis time there is an enrollee (hereafter referred to as identifiedenrollee) identified as the same person as the authentication objectuser, then the authentication is regarded as successful with theidentified enrollee obtained as an identification result. If there isn'tan identified enrollee, then the authentication is regarded asunsuccessful. As examples of a biometric authentication system utilizingthe 1:N identification, a service record management system and a systemfor conducting credit account settlement on the basis of biometricauthentication without using a credit card (hereafter referred to ascard-less credit account settlement system) can be mentioned. The 1:Nidentification has an advantage of high convenience because theauthentication object user need not exhibit a card or the like. However,the 1:N identification has a problem that as the number N of enrolleesincreases the authentication accuracy is degraded and the authenticationtime increases because the number of identification objects increases.

According to K. Nandakumar. et al., “Fusion in MultibiometricIdentification Systems: What about the Missing Data?,” Proc. ICB, pp.743-752, 2009 (Document 1), in the 1:N identification, a posteriorprobability that the authentication object user will be each enrollee iscalculated on the basis of obtained scores and the user is identified byusing the posterior probability.

According to JP-A-H11-296531 ([0008], [0012], FIG. 1, Document 2), whichcorresponds to U.S. Pat. No. 6,229,922 B1, Sasakawa et al., a similaritytable using similarities each of which is a degree of coincidencebetween two registered data obtained by calculating it for all possiblecombinations in selecting two out of a plurality of registered data isgenerated beforehand, and a sequence of registered data to be readsubsequently is controlled by using a matching degree between matchingdata to be matched and registered data and the similarity table. At thistime, it is also possible to discontinue the matching processing if thenumber of times of matching exceeds a predetermined threshold.

SUMMARY

It is possible to implement higher precision by applying the techniqueaccording to Document 1 to the 1:N identification and implement fasterspeed by applying the technique according to Document 2 to the 1:Nidentification. However, a technique for reconciling the higherprecision and higher speed of the 1:N identification has not beenproposed so far.

It is also conceivable to combine the technique according to Document 1with the technique according to Document 2. However, deciding in thetechnique according to Document 2 to discontinue matching processing attime when the number of times of matching has exceeded the predeterminedthreshold poses a problem that scores cannot be found for remainingenrollees who are not subjected to matching and the posteriorprobability cannot be found suitably. Furthermore, deciding in thetechnique according to Document 2 not to discontinue the matchingprocessing even if the number of times of matching has exceeded thepredetermined threshold poses a problem that it becomes necessary toconduct the matching for all enrollees and a faster speed cannot beimplemented at all in the worst case.

Herein, a 1:N identification technique which reconciles a fasterprecision and a faster speed will be disclosed.

In accordance with one aspect of the disclosure, a biometricauthentication system includes a database retaining an enrollee ID foreach of enrollees, registered templates of biometric information of atleast one kind for each of enrollees, and a score table, a priorprobability setting function for setting prior probabilities that anauthentication object user will be the same person as the respectiveenrollees, at least one biometric information input sensor for acquiringbiometric information of at least one kind from the authenticationobject sensor, a feature extraction function for extracting a featurefrom the acquired biometric information, a 1:N fast matching functionfor using the registered templates respectively of the enrollees withrespect to the feature of the authentication object user, rearranging asequence of the registered templates to be matched while referring tothe score table, thereby conducting 1:N fast matching, and discontinuingthe matching processing when the number of times of matching hasexceeded a predetermined threshold, a delta score calculation functionfor calculating a delta score by using a score obtained by the 1:N fastmatching and using the score table, a posterior probability calculationfunction for calculating posterior probabilities respectively of theenrollees on the basis of the score and the delta score, and anauthentication object user identification function for conductingidentification of the authentication object user by comparing inmagnitude each of the posterior probabilities with a threshold. (Deltais expressed as ‘Δ’ in expressions.)

In accordance with an aspect of the disclosure, matching with Kregistered templates where K is less than N is conducted and theposterior probability is calculated by using the score and delta scores.Therefore, it becomes possible to find the posterior probability morestrictly as compared with the conventional technique which conducts 1:Nidentification using the score or the delta score. Therefore, it becomespossible to raise the authentication precision while holding down theauthentication time required since biometric information is input untilan authentication result is returned to within a certain fixed value. Asa result, an effect that the convenience and safety are improved isobtained.

The above-described mode can be applied to all 1:N identificationsystems which conduct confirmation of the person in question by usingthe scores. Therefore, the mode can be applied to all modalities such asa fingerprint, an iris or a vein, and can be applied to matchingalgorithms of all kinds which output a score. More specifically, themode can be applied to all applications using biometric authenticationsuch as physical access control, time and attendance management or PClog-in. The “modality” means kinds of biometric information which can beacquired by one sensor.

It becomes possible to raise the authentication precision while keepingthe authentication time in biometric authentication short. As a result,it becomes possible to improve the convenience and safety.

Other objects, features and advantages of the invention will becomeapparent from the following description of the embodiments of theinvention taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram exemplifying a functional configuration infirst and second embodiments.

FIG. 2 is a block diagram exemplifying a hardware configuration in thefirst and second embodiments.

FIG. 3 is a flow diagram exemplifying authentication processing in thefirst embodiment.

FIG. 4 is a flow diagram exemplifying authentication processing in thesecond embodiment.

FIG. 5 is a diagram exemplifying a configuration of a score table in thefirst and second embodiments.

EMBODIMENTS

Hereafter, embodiments will be described with reference to the drawings.

1. First Embodiment

A biometric authentication system in a first embodiment is a biometricauthentication system which conducts 1:N identification between anauthentication object user and N enrollees each time the authenticationobject user inputs biometric information.

By the way, it is supposed that the score in the present embodiment isdefined by using a similarity. In other words, as two features arealike, the score becomes greater in value. Conversely, if the score isdefined by using an unsimilarity, then the score assumes a smaller valueas the two features are alike.

FIG. 1 shows a configuration example of the biometric authenticationsystem. This system is configured to include an authentication clientapparatus (hereafter referred to as authentication client) 100 whichconducts direct exchange with an authentication object user, anauthentication server apparatus (hereafter referred to as authenticationserver) 110 which conducts 1:N identification, and a network 130. Thenetwork 130 may use a network such as a WAN or a LAN, inter-devicecommunication using the USB or IEEE 1394, or wireless communication suchas a portable telephone network or short distance radio.

For example, in the case of a card-less credit account settlementsystem, a configuration in which the authentication client 100 is anauthentication apparatus placed in a member store, the authenticationserver 110 is a server placed in a data center, and the network 130 isthe Internet is conceivable. In the case of an entrance-leavingmanagement system, a configuration in which the authentication client100 is an authentication apparatus placed at a building entrance or in aroom, the authentication server 110 is a server placed in a server room,and the network 130 is an intra-enterprise intranet is conceivable.Although the authentication client 100 is separated from theauthentication server 110 here, they may be put together as oneapparatus.

The authentication client 100 is configured to include a biometricinformation input sensors 101 respectively capable of acquiringbiometric information 1 to biometric information M of an authenticationobject user, a feature extraction function 102 for extracting a featurefrom the acquired biometric information, a communication I/F 103, and afinal identification function 104 for conducting final identification onthe basis of an identification result of the authentication object usersent from the authentication server 110. The number M of kinds ofbiometric information may be one (M=1) or a plurality (M>1). Theplurality of kinds of biometric information may be formed of differentmodalities such as, for example, a fingerprint, an iris, and avoiceprint, or may be formed of different regions of the same modalitysuch as a fingerprint of a forefinger, a fingerprint of a middle finger,and a fingerprint of a medical finger. If the plurality kinds ofbiometric information are formed of different regions of the samemodality, one input sensor suffices.

The authentication server 110 is configured to include a priorprobability setting function 111 for setting a probability of theauthentication object user being the same person as each enrollee(hereafter referred to as prior probability, which may include aprobability of the authentication object user being a non-enrollee)before a score is obtained, a 1:N fast matching function 112 forconducting 1:N fast matching by using a feature of the authenticationobject user sent from the authentication client 100, a delta scorecalculation function 113 for calculating a delta score which is adistance between scores on the basis of a score obtained as a result ofthe 1:N matching and a score table described later, a posteriorprobability calculation function 114 for calculating a probability ofthe authentication object user being the same person as each enrollee(hereafter referred to as posterior probability, which may be aprobability of the authentication object user being a non-enrollee) byusing the scores and the delta scores, an authentication object useridentification function 115 for identifying the authentication objectuser as the same person as an enrollee or a non-enrollee on the basis ofthe posterior probability, a communication I/F 116, and a database 120.

The database 120 retains enrollee data 121 for N enrollees and a scoretable 124 which stores scores between registered templates. The enrolleedata 121 is configured to include an enrollee ID 122 and registeredtemplates 123 of biometric information 1 to biometric information M.

The score table 124 retains a score r_(ij) (1=<i=<N, 1=<j=<N, i is notequal to j) between registered templates of the ith enrollee and the jthenrollee every kind of biometric information. FIG. 5 shows aconfiguration diagram of the score table 124. Although this is an N by Nmatrix, a part thereof may be retained as the score table 124. Forexample, it is also possible to select L (<N) registered templates outof N registered templates as representatives and retain (a total of L*N)scores between the L registered templates and the N registered templates(* means multiplication). The score table 124 is generated since Nenrollees are registered until authentication is conducted.

FIG. 2 shows a hardware configuration for implementing theauthentication client 100 and the authentication server 110. Theseapparatuses can be configured by using a typical computer which includesa CPU 200, a memory 201, a secondary storage device 202 such as a HD, aninput device 203 such as a keyboard, an output device 204 such as adisplay device and a printer, and a communication device 205.

In addition, the functions, the sensors and the communication I/Fincluded in each apparatus are implemented on the computer by executionof a program by the CPU 200 or cooperation with hardware. Each programmay be previously stored in the secondary storage device 202 in thecomputer, or may be introduced from another device to the secondarystorage device 202 via an external interface which is not illustrated orthe communication device 205 and a medium which can be utilized by thecomputer. The “medium” means, for example, a storage medium which can beattached to or detached from an input/output interface or acommunication medium (i.e., a wired, wireless or optical network, or acarrier wave or a digital signal propagated through the network). Thecalculated prior probability and posterior probability are retained inthe memory 201.

FIG. 3 shows a processing procedure and a data flow of authentication inthe present embodiment.

The prior probability setting function 111 sets a prior probabilityP(v=u_(n)) of each enrollee u_(n) (1=<n=<N) and a prior probabilityP(v=u₀) of a non-enrollee u₀ (step S301). The prior probabilities may beset to be equal as represented by the following expressions.

P(v=u _(n))=1/(N+1)(1=<n=<N)   (Expression 1)

P(v=u ₀)=1/(N+1)   (Expression 2)

Or the prior probabilities of each enrollee and the non-enrollee may beupdated by using past final identification results as disclosed inJP-A-2009-289253 (corresponding to US2009/0289760A1, Murakami et al.) bythe present applicant (hereafter referred to as Document 3). Forexample, according to a method, final identification results(“successful authentication,” “impersonation,” or “unsuccessfulauthentication”) of past D times are retained in the database 120.Supposing that the number of times the final identification resultbecame “impersonation” in the past authentication processing of D timesis D₀, the prior probability P(v=u_(n)) of each enrollee u_(n) and theprior probability P(v=u₀) of the non-enrollee u₀ are set as representedby the following expressions.

P(v=u _(n))=(1−D ₀ /D)/(N+1) (1=n=<N)   (Expression 3)

P(v=u ₀)=(N*D ₀ /D+1)/(N+1)   (Expression 4)

One of M biometric information input sensors 101 acquires biometricinformation of the authentication object user v. It is now supposed thatthe number of times the authentication object user v has input biometricinformation so far is t (step S302).

The feature extraction function 102 extracts a feature from eachacquired biometric information (step S303).

The communication I/F 103 transmits each feature to the authenticationserver 110 (step S304).

The 1:N fast matching function 112 conducts 1:N matching between thefeature sent from the authentication client 100 and registered templates123 of K (<N) persons where K is a predetermined threshold among Nenrollees. As a result, scores for K enrollees are obtained. The valueof K may differ every sent feature. Supposing that a number of anenrollee in the ith (where 1=<i=<K) matching is m(i) (1=<m(i)=<N), thescore of the enrollee is represented by s_(tm(i)) (where t is the numberof times of inputting as described earlier) (step S305).

By conducting matching for K (<N) enrollees in this way, 1:N matching ina shorter time becomes possible as compared with the case where matchingis conducted for N enrollees. As a result, authentication can beconducted faster and an effect of improved convenience is obtained.

By the way, when conducting the 1:N matching, the sequence of theregistered templates 123 to be matched may be rearranged by referring tothe whole or a part of obtained scores and the score table 124 whileconducting the matching. Specifically, the same technique as thataccording to Document 2 may be used. Or any one of similarity searchtechniques described in E. Chavez et al., “Seaching in Metric Spaces”,ACM Computing Surveys, vol. 33, no. 3, pp. 273-321 (2001) may be used.Furthermore, the sequence of registered templates 123 to be matched maybe rearranged by using scores and delta scores described later, whichare obtained until now.

The delta score calculation function 113 calculates a delta score whichrepresents how two scores (scalars) differ by using the obtained scoreand the score table 124. Specifically, for example,

Δs _(tim(j))=|s _(tm(j)) −r _(im(j))|(1=<i=<N, 1=<j=<K, i is not equalto j)   (Expression 5)

is found. In Expression 5, the delta score is defined as an absolutevalue of a difference between two scores. However, powers or roots ofthe two score values, two score values multiplied respectively byconstants, or the sum of the two score values may be used in thedefinition of the delta score. If a part of the N by N matrix isretained as the score table, a part of delta scores cannot be calculatedin some cases. The posterior probability calculation method in this casewill be described later. (step S306).

The posterior probability calculation function 114 calculates aposterior probability P(v=u_(n)|S₁, . . . , S_(t), ΔS₁, ΔS_(t)) of eachenrollee u_(n) (1=<n=<N) and a posterior probability P(v=u₀|S₁, . . . ,S_(t), ΔS₁, ΔS_(t) of a non-enrollee u₀ by using the scores and thedelta scores obtained so far. Here,

S _(t) ={s _(tm(i))|1=<i=<K}  (Expression 6)

ΔS _(t) ={Δs _(tim(j))|1=<i=<N, 1=<j=<K, i is not equal toj}  (Expression 7)

(step S307). Details of a method for calculating the posteriorprobability will be described later.

The authentication object user identification function 115 identifiesthe authentication object user v by comparing the posterior probabilityobtained at the step S307 with a predetermined threshold A.Specifically, if there is at least one posterior probability exceedingthe threshold A among the posterior probabilities P(v=u_(n)|S₁, . . . ,S_(t), ΔS₁, . . . , ΔS_(t)) of respective enrollees u_(n) (1=<n=<N) andthe posterior probability P(v=u₀|S₁, . . . , S_(t), ΔS₁, . . . , ΔS_(t))of a non-enrollee u₀, an enrollee or a non-enrollee who has implementeda maximum value is regarded as an identification result. If there is noposterior probability exceeding the threshold A, the identification isregarded as unsuccessful (step S308).

The communication I/F 116 transmits the identification result obtainedat the step S308 to the authentication client 100. Specifically, if theidentification result of the authentication object user is an enrollee,the communication I/F 116 transmits an identified enrollee ID 122. Ifthe identification result of the authentication object user is anon-enrollee, the communication I/F 116 transmits “impersonation.” Ifthe identification is unsuccessful, the communication I/F 116 transmits“unsuccessful identification” (step S309).

If the identification result of the authentication object user sent fromthe authentication server 110 is the enrollee ID 122, the finalidentification function 104 determines the final result to be“successful authentication.” If the identification result of theauthentication object user is “impersonation,” the final identificationfunction 104 determines the final result to be “impersonation.” If theidentification result of the authentication object user is “unsuccessfulidentification,” the processing proceeds to step S311 (step S310). If“impersonation” is determined to be the final result, penal regulationsto the authentication object user such as temporary lock of theauthentication client 100 or alarm sounding may be provided as describedin Document 3. An effect obtained by providing penal regulations to theauthentication object user will be described later.

If the number t of times of biometric information inputting has reachedM, the final identification function 104 determines the final result tobe “unsuccessful authentication.” Unless the number t of times ofbiometric information inputting has reached M, the processing returns tothe step S302 (step S311). If “unsuccessful authentication” isdetermined to be the final result, the authentication object user may beordered to retry the authentication.

Hereafter, the method for calculating the posterior probability at thestep S307 will be described in detail.

Supposing that a set of scores at respective inputs S₁, . . . , S_(t) isindependent and a set of delta scores ΔS₁, . . . , ΔS_(t) isindependent, the posterior probability P(v=u_(k)|S₁, S_(t), ΔS₁, . . . ,ΔS_(t))(0=<N) can be represented by Expression 8 according to the Bayestheory.

$\begin{matrix}{{{P\left( {{v = \left. u_{k} \middle| S_{1} \right.},\ldots \mspace{14mu},S_{t},{\Delta \; S_{1}},\ldots \mspace{14mu},{\Delta \; S_{t}}} \right)} = \frac{{P\left( {{v = \left. u_{k} \middle| S_{1} \right.},\ldots \mspace{14mu},S_{t - 1},{\Delta \; S_{1}},\ldots \mspace{14mu},{\Delta \; S_{t - 1}}} \right)}Z_{tk}}{\sum\limits_{n = 0}^{N}{{P\left( {{v = \left. u_{k} \middle| S_{1} \right.},\ldots \mspace{14mu},S_{t - 1},{\Delta \; S_{1}},\ldots \mspace{14mu},{\Delta \; S_{t - 1}}} \right)}Z_{tn}}}}\mspace{20mu} {{Here},}} & \left( {{Expression}\mspace{14mu} 8} \right) \\{\mspace{20mu} {Z_{tk} = \frac{P\left( {S_{t},{\left. {\Delta \; S_{t}} \middle| v \right. = u_{k}}} \right)}{P\left( {S_{t},{\left. {\Delta \; S_{t}} \middle| v \right. = u_{0}}} \right)}}} & \left( {{Expression}\mspace{14mu} 9} \right)\end{matrix}$

Z_(tk) is referred to as likelihood rate. Since P(v=u_(k)|S₁, . . . ,S_(t−1), ΔS₁, . . . , ΔS_(t−1)) is a posterior probability at the timewhen up to the last feature is obtained, the posterior probabilityP(v=u_(k)|S₁, . . . , S_(t), ΔS₁, . . , ΔS_(t)) can be found recursivelyby using the prior probability P(v=u_(k)) and Z_(tk).

It is supposed that respective scores are independent and the followingexpressions hold true

P(s _(tm(i)) |v=u _(k))=f(s _(tm(i)))(when m(i)=k)   (Expression 10)

P(s _(tm(i)) |v=u _(k))=g(s_(tm(i)))(when m(i) is not equal to k)  (Expression 11)

where 0=<k=<N. In other words, it is supposed that scores s between theperson in question and the person in question follow the genuinedistribution f(s) and scores s between others follow impostordistribution g(s).

Furthermore, it is supposed that respective delta scores are independentand the following expressions hold true

P(Δs _(tim(j)) |v=u _(k))=f′(s _(tm(i)))(when i=k)   (Expression 12)

P(Δs _(tim(j)) |v=u _(k))=g′(s _(tm(i)))(when i is not equal to k)  (Expression 13)

where 0=<k=<N. In other words, it is supposed that delta scores Δsbetween the person in question and the person in question follow thegenuine distribution f′(s) and delta scores Δs between others followimpostor distribution g′(s). In the ensuing description, it is assumedthat these suppositions hold true.

If it is supposed that the scores and the delta scores are completelyindependent, the likelihood rate Z_(tk) (0=<k=<N) can be found asfollows:

$\begin{matrix}\begin{matrix}{Z_{tk} = \frac{P\left( {S_{t},{\left. {\Delta \; S_{t}} \middle| v \right. = u_{k}}} \right)}{P\left( {S_{t},{\left. {\Delta \; S_{t}} \middle| v \right. = u_{0}}} \right)}} \\{= \frac{\prod\limits_{i = 1}^{K}{{P\left( {\left. s_{{tm}{(i)}} \middle| v \right. = u_{k}} \right)}{\prod\limits_{i = 1}^{N}{\prod\limits_{j = 1}^{K}{P\left( {\left. {\Delta \; s_{\tau \; {{im}{(j)}}}} \middle| v \right. = u_{k}} \right)}}}}}{\prod\limits_{i = 1}^{K}{{P\left( {\left. s_{{tm}{(i)}} \middle| v \right. = u_{0}} \right)}{\prod\limits_{i = 1}^{N}{\prod\limits_{j = 1}^{K}{P\left( {\left. {\Delta \; s_{\tau \; i\; {m{(j)}}}} \middle| v \right. = u_{0}} \right)}}}}}} \\{= \left\{ \begin{matrix}\begin{matrix}f & {{\left( s_{tk} \right)/{g\left( s_{tk}\; \right)}}{\prod\limits_{{j = 1},{j \neq k}}^{K}{{f^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}/{g^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}}}}\end{matrix} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}} \\{{with}\mspace{14mu} {the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {conducted}}\end{pmatrix} \\{{\prod\limits_{j = 1}^{K}{{f^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}/{g^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}}}\mspace{194mu}} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}} \\{{with}\mspace{14mu} {the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {conducted}}\end{pmatrix} \\\begin{matrix}1 & {\left( {{{when}\mspace{14mu} k} = 0} \right)\mspace{310mu}}\end{matrix}\end{matrix} \right.}\end{matrix} & \left( {{Expression}\mspace{14mu} 14} \right)\end{matrix}$

As for f(s), g(s), f′ (Δs) and g′(Δs), a model such as the normaldistribution, gamma distribution or beta beta binomial distribution issupposed and the authentication server is caused to learn parameters byusing a technique such as the maximum likelihood estimation, the MAPestimation, or the Bayes estimation since N enrollees are registereduntil authentication is conducted.

Or f(s)/g(s) and f′(Δs)/g′(Δs) may be learned directly by using logisticregression. Although f(s) and g(s) are caused to be learned beforehandevery modality, the same distribution may be used if different regionsof the same modality are used.

Furthermore, f(s), g(s), f′ (Δs), g′(Δs), f(s)/g(s) and f′ (Δs)/g′(Δs)may be learned in common to all users, may be learned every user, or maybe learned every pair of the authentication object user and an enrollee.

Supposing that the scores and the delta scores are completely dependent,the delta scores are not used for enrollees subjected to the matching,and a number of an enrollee which is not subjected to the matching isn(i) (1=<i=<N−K, 1=<n(i)=<N), the likelihood rate Z_(tk) (0=<k=<N) canbe found by using the following expression.

$\begin{matrix}\begin{matrix}{Z_{tk} = \frac{P\left( {S_{t},{\left. {\Delta \; S_{t}} \middle| v \right. = u_{k}}} \right)}{P\left( {S_{t},{\left. {\Delta \; S_{t}} \middle| v \right. = u_{0}}} \right)}} \\{= \frac{\prod\limits_{i = 1}^{K}{{P\left( {\left. s_{{tm}{(i)}} \middle| v \right. = u_{k}} \right)}{\prod\limits_{i = 1}^{N - K}{\prod\limits_{j = 1}^{K}{P\left( {\left. {\Delta \; s_{\tau \; {n{(i)}}{m{(j)}}}} \middle| v \right. = u_{k}} \right)}}}}}{\prod\limits_{i = 1}^{K}{{P\left( {\left. s_{{tm}{(i)}} \middle| v \right. = u_{0}} \right)}{\prod\limits_{i = 1}^{N - K}{\prod\limits_{j = 1}^{K}{P\left( {\left. {\Delta \; s_{\tau \; {n{(i)}}{m{(j)}}}} \middle| v \right. = u_{0}} \right)}}}}}} \\{= \left\{ \begin{matrix}\begin{matrix}f & {{\left( s_{tk} \right)/{g\left( s_{tk} \right)}}\mspace{310mu}}\end{matrix} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}} \\{{with}\mspace{14mu} {the}\mspace{20mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {conducted}}\end{pmatrix} \\{{\prod\limits_{j = 1}^{K}{{f^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}/{g^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}}}\mspace{169mu}} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}} \\{{with}\mspace{14mu} {the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {conducted}}\end{pmatrix} \\\begin{matrix}1 & {\left( {{{when}\mspace{14mu} k} = 0} \right)\mspace{290mu}}\end{matrix}\end{matrix} \right.}\end{matrix} & \left( {{Expression}\mspace{14mu} 15} \right)\end{matrix}$

Or supposing that the scores and the delta scores are independent tosome degree, the likelihood rate Z_(tk) (0=<k=<N) can be found by usingthe following expression.

$\begin{matrix}{Z_{tk} = \left\{ \begin{matrix}\begin{matrix}f & {{{\left( s_{tk} \right)/{g\left( s_{tk} \right)}} \times \left\lbrack {\prod\limits_{{j = 1},{j \neq k}}^{K}\frac{f^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}{g^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}} \right\rbrack^{a}}\mspace{121mu}}\end{matrix} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}\mspace{14mu} {with}} \\{{the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {conducted}}\end{pmatrix} \\{{\prod\limits_{j = 1}^{K}{{f^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}/{g^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}}}\mspace{236mu}} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}\mspace{14mu} {with}} \\{{the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {conducted}}\end{pmatrix} \\\begin{matrix}1 & {\left( {{{when}\mspace{14mu} k} = 0} \right)\mspace{349mu}}\end{matrix}\end{matrix} \right.} & \left( {{Expression}\mspace{14mu} 16} \right)\end{matrix}$

The parameter a (0=<a=<1) is a parameter which indicates the degree ofindependence of the scores and delta scores. When a=1, the expressioncoincides with the expression obtained by supposing that the scores andthe delta scores are completely independent. When a=0, the expressioncoincides with the expression obtained by supposing that the scores andthe delta scores are completely dependent. In other words, Expression 16coincides with Expression 14 when a=1, whereas Expression 16 coincideswith Expression 15 when a=0.

Or the likelihood rate Z_(tk) (0=<k=<N) may be found by using thefollowing expression.

$\begin{matrix}{Z_{tk} = \left\{ \begin{matrix}\begin{matrix}f & {{{\left( s_{tk} \right)/{g\left( s_{tk} \right)}} \times \left\lbrack {\prod\limits_{{j = 1},{j \neq k}}^{K}\frac{f^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}{g^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}} \right\rbrack^{{ab}_{1}}}\mspace{34mu}}\end{matrix} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}} \\{{with}\mspace{14mu} {the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {conducted}}\end{pmatrix} \\{\left\lbrack {\prod\limits_{j = 1}^{K}{{f^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}/{g^{\prime}\left( {\Delta \; s_{{tkm}{(j)}}} \right)}}} \right\rbrack^{b_{2}}\mspace{135mu}} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}} \\{{with}\mspace{14mu} {the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {conducted}}\end{pmatrix} \\\begin{matrix}1 & {\left( {{{when}\mspace{14mu} k} = 0} \right)\mspace{295mu}}\end{matrix}\end{matrix} \right.} & \left( {{Expression}\mspace{14mu} 17} \right)\end{matrix}$

Parameters b₁ and b₂ (b₁=>0, b₂=>0) are parameters for adjusting theinfluence of f′(Δs)/g′(Δs) upon the likelihood rate Z_(tk), i.e., theinfluence of the delta scores upon the likelihood rate Z_(tk). As b₁ andb₂ become greater, the influence becomes more intense. When b₁=b₂=1,Expression 17 coincides with Expression 16.

When retaining a part of an N by N matrix as the score table 124, a partof delta scores Δs cannot be calculated in some cases. At that time, amethod of setting the corresponding f′(Δs)/g′(Δs) equal to 1 isconceivable. By doing so, it becomes possible to calculate thelikelihood rate Z_(tk), and consequently it becomes possible tocalculate the posterior probability as well.

In the present embodiment, the matching processing is discontinued attime when the number of times of matching has exceeded the predeterminedthreshold K and thereafter the likelihood rate and the posteriorprobability are calculated by using both the scores and the delta scoresas observed data, in this way.

In Document 1, a method of setting f(s)/g(s) equal to 1 for an enrolleehaving a score s which cannot be found is proposed. When this techniqueis used, the likelihood rate Z_(tk) (0=<k=<N) is found by using thefollowing expression.

$\begin{matrix}{Z_{tk} = \left\{ \begin{matrix}\begin{matrix}f & {{\left( s_{tk} \right)/{g\left( s_{tk} \right)}}\mspace{346mu}}\end{matrix} \\\begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}} \\{{with}\mspace{14mu} {the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {conducted}}\end{pmatrix} \\\begin{matrix}1 & \begin{pmatrix}{{when}\mspace{14mu} k\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {equal}\mspace{14mu} {to}\mspace{14mu} 0\mspace{14mu} {and}\mspace{14mu} {matching}} \\{{with}\mspace{14mu} {the}\mspace{14mu} {kth}\mspace{14mu} {enrollee}\mspace{14mu} {is}\mspace{14mu} {not}\mspace{14mu} {conducted}}\end{pmatrix}\end{matrix} \\\begin{matrix}1 & {\left( {{{when}\mspace{14mu} k} = 0} \right)\mspace{326mu}}\end{matrix}\end{matrix} \right.} & \left( {{Expression}\mspace{14mu} 18} \right)\end{matrix}$

This corresponds to the case where b₁=b₂=0 is set in Expression 17,i.e., the case where it is supposed that there is no influence of thedelta scores upon the likelihood rate Z_(tk) in Expression 17. In thiscase, however, the likelihood rate is not found strictly by using thedelta scores for the enrollee having a score which is not found.Therefore, then the posterior probability cannot be found strictly.

On the other hand, in the present embodiment, the likelihood rate can befound more strictly as compared with the case where the likelihood rateis set equal to 1, by using the delta scores even for an enrollee havinga score which cannot be found. As a result, the posterior probabilitycan also be found more strictly.

Furthermore, in the present embodiment, the posterior probability iscalculated by using the scores and the delta scores. Therefore, itbecomes possible to find the posterior probability more strictly ascompared with the conventional technique of conducting 1:Nidentification by using the scores or the delta scores. In the presentembodiment, therefore, it becomes possible to enhance the authenticationprecision while limiting an authentication time required since biometricinformation is input until an authentication result is returned towithin a certain fixed value. As a result, an effect that theconvenience and safety are improved is obtained.

Hereafter, the method of rearranging the sequence of registeredtemplates 123 to be matched by using the scores and the delta scoredescribed later which are obtained so far at the step S305 will bedescribed in detail. For example, in a conceivable method, a likelihoodrate Z_(t−lk) (1=<k=<N) found at the (t−1)th input is substituted into alikelihood rate Z_(tk) (1=<k=<N) and the likelihood rate Z_(tk)(1=<k=<N) is also always updated by using the obtained scores and deltascores while conducting matching in the descending order of the value.For example, in the case where Expression 14 is used as the likelihoodrate Z_(tk) (1=<k=<N), matching should be conducted in the followingsequence.

1. A likelihood rate Z_(t−lk) (1=<k=<N) found at the (t−1)th input issubstituted into a likelihood rate Z_(tk) (1=<k=<N) (Z_(tk) is set toZ_(tk)=1 (1=<k=<N) when t=1). Furthermore, j is set to j=1.

2. Matching is conducted with an enrollee having the highest likelihoodrate Z_(tk) (1=<k=<N) among enrollees who are not yet subjected tomatching, and a score s_(tm(j)) is found (where m(j) is a number of anenrollee subjected to matching). If there are a plurality of enrolleeshaving the highest likelihood rate Z_(tk), matching may be conductedwith any of them.

3. Then, f(s_(tm(j)))/g(s_(tm(j))) is added to a likelihood rateZ_(tm(j)) of the m(j)th enrollee.

4. Then, Δs_(tkm(j))=|s_(tm(j))−r_(km(j))|(1=<k=<N, k=<N, k is not equalto m(j)) is found while referring to the score table 124. Andf′(Δs_(tkm(j)))/g′(Δs_(tkm(j))) is added to the likelihood rate Z_(tk)of all enrollees k (k is not equal to m(j)) other than the m(j)thenrollee.

5. Unity is added to j, and return to 2 is conducted.

According to the above-described method, it becomes possible to find thelikelihood rate Z_(tk) (1=<k=<N) by using the scores and the deltascores obtained until then, every time matching is conducted and conductthe next matching with an enrollee having the highest value of thelikelihood rate Z_(tk). Since the possibility that the enrollee having ahigh likelihood rate is the person in question is high at this time, itbecomes possible to conduct matching with the person in question at anearlier stage.

Furthermore, in this method, the matching sequence is rearranged byusing the scores and the delta scores obtained in the past (until the(t−1)th time) as well. This results in an effect that a farther faster1:N fast matching can be implemented as compared with the method ofrearranging the matching sequence without using the scores and the deltascores obtained in the past (until the (t−1)th time) (for example, themethod of always setting Z_(tk)=1 (1=<k=<N) in the above-described firstprocessing).

In the above-described example, the likelihood rate is calculated byusing Expression 14. Alternatively, a different expression such asExpression 15 or Expression 16 may be used. In the above-describedexample, the likelihood rate is updated. Alternatively, a different onesuch as the posterior probability may be updated.

In Document 1, the posterior probability P(v=u₀|S₁, . . . , S_(t), ΔS₁,. . . , ΔS_(t)) of a non-enrollee u₀ is not calculated. When anunenrollee attempts impersonation in this case, small scores (here,similarities) are obtained for all enrollees. If one of them is largerthan others, however, the possibility that the posterior probabilitycorresponding to it assumes a large value is high. This results in aproblem of high possibility that “successful authentication” isidentified. On the other hand, in the present embodiment, the posteriorprobability P(v=u₀|S₁, . . . , S_(t), ΔS₁, . . . , ΔS_(t)) of anon-enrollee u₀ is also calculated. If the non-enrollee attemptsimpersonation in this case and small scores (here, similarities) areobtained for all enrollees, then Z_(tk) (1=<k=<N) of every enrolleebecomes a small value (<<1) and consequently the posterior probabilityP(v=u₀|S₁, . . . , S_(t), ΔS₁, . . . , ΔS_(t)) of the non-enrollee u₀becomes large. As a result, the possibility that “successfulauthentication” is identified is low, whereas the possibility that“impersonation” is identified is high. As a result, an effect that thesafety is further improved is obtained.

In addition, in the present embodiment, “impersonation” is determined tobe the final result when the authentication object user is identified asa non-enrollee. When a decision cannot be made who is the authenticationobject user, “unsuccessful authentication” is determined to be the finalresult. A clear distinction is made between these two final results.When a non-enrollee attempts impersonation, therefore, penal regulationsto the authentication object user such as temporary lock of theauthentication client 100 or alarm sounding can be provided. When“unsuccessful authentication” is determined to be the final result,penal regulations can be adapted to be not provided. As a result, aneffect that the safety can be further improved is obtained.

2. Second Embodiment

A biometric authentication system in a second embodiment is a biometricauthentication system which conducts 1:N identification between anauthentication object user and N enrollees after the authenticationobject user is caused to input M (=>1) pieces of biometric information.By the way, in the present embodiment as well, it is supposed that thescore is defined by using a similarity. In other words, as two featureare alike, the score becomes greater in value.

A configuration example of the biometric authentication system in thepresent embodiment is the same as that shown in FIG. 1.

A hardware configuration of the authentication client 100 and theauthentication server 110 in the present embodiment is the same as thatshown in FIG. 2.

FIG. 4 shows a processing procedure and a data flow of authentication inthe present embodiment. Here, a difference of them from those in FIG. 3will be described. By the way, in the present processing procedure, thestep S311 is eliminated.

Each of M biometric information input sensors 101 acquires biometricinformation of the authentication object user v. As a result, M piecesof biometric information are obtained (step S302).

The feature extraction function 102 extracts a feature from eachacquired biometric information (step S303).

The communication I/F 103 transmits each feature to the authenticationserver 110 (step S304).

The 1:N fast matching function 112 conducts 1:N fast matching betweeneach feature sent from the authentication client 100 and registeredtemplates 123 of N enrollees while referring to the score table 124 onthe basis of the distance index method. It is supposed that as a resultas regards tth (where 1=<t=<M) feature among respective sent featurescores for K (=<N) users are obtained. The value of K may differ everysent feature. Supposing that a number of an enrollee in the ith (where1=<i=<K) matching is m(i) (1=<m(i)=<N), the score of the enrollee isrepresented by s_(tm(i)) (where t is a number of times of inputting asdescribed earlier) (step S305).

The delta score calculation function 113 calculates a delta score byusing the obtained score and the score table 124. Specifically,

Δs _(tim(j)) =|s _(tm(j)) −r _(im(j))|(1=t=<M, 1=<i=<N, 1=<j=<K, i isnot equal to j)   (Expression 19)

is found (step S306).

The posterior probability calculation function 114 calculates aposterior probability P(v=u_(n)|S₁, . . . , S_(M), ΔS₁, . . . , ΔS_(M))of each enrollee u_(n) (1=<n=<N) and a posterior probability P(v=u₀|S₁,. . . , S_(M), ΔS₁, . . . , ΔS_(M)) of a non-enrollee u₀ by using thescores and the Δ scores obtained so far. Here,

S _(t) ={s _(tm(i))|1=<i=<K}(1=<t=<M)   (Expression 20)

ΔS _(t) ={s _(tim(j))|1=<i=<N, 1=<j=<K, i is not equal to j}(1=<t=<M)  (Expression 21)

(step S307). The method for calculating the posterior probability is thesame as that in the first embodiment.

The authentication object user identification function 115 identifiesthe authentication object user v by comparing the posterior probabilityobtained at the step S307 with a predetermined threshold A.Specifically, if there is at least one posterior probability exceedingthe threshold A among the posterior probabilities P(v=u_(n)|S₁, . . . ,S_(M), ΔS₁, . . . , ΔS_(M))(1=<n=<N) and the posterior probabilityP(v=u₀|S₁, . . . , S_(M), ΔS₁, . . . , ΔS_(M)), u_(n) who hasimplemented a maximum value is regarded as an identification result. Ifthere is no posterior probability exceeding the threshold A, theidentification is regarded as unsuccessful (step S308).

If the identification result of the authentication object user sent fromthe authentication server 110 is the enrollee ID 122, the finalidentification function 104 determines the final result to be“successful authentication.” If the identification result of theauthentication object user is “impersonation,” the final identificationfunction 104 determines the final result to be “impersonation.” If theidentification result of the authentication object user is “unsuccessfulidentification,” the final identification function 104 determines thefinal result to be “unsuccessful authentication.” If “unsuccessfulauthentication” is determined to be the final result, the authenticationobject user may be ordered to retry the authentication (step S310).

It should be further understood by those skilled in the art thatalthough the foregoing description has been made on embodiments of theinvention, the invention is not limited thereto and various changes andmodifications may be made without departing from the spirit of theinvention and the scope of the appended claims.

1. A biometric authentication system comprising: a database retaining anenrollee ID for each of N enrollees, registered templates of biometricinformation of at least one kind for each of N enrollees, and a scoretable for recording scores, each of the scores representing a similaritybetween a registered template and a corresponding registered template ofanother enrollee; a prior probability setting function for setting priorprobabilities that an authentication object user will be same person asthe respective enrollees; biometric information input sensors foracquiring biometric information of at least one kind from theauthentication object sensor; a feature extraction function forextracting a feature from the acquired biometric information; a 1:N fastmatching function for matching the feature of the authentication objectuser with the registered templates of the enrollees numbering apredetermined threshold K (K<N); a delta score calculation function forcalculating a delta score which represents how much two scores differfrom each other, by using a score obtained for each of the registeredtemplates by the 1:N fast matching and using the score table; aposterior probability calculation function for calculating posteriorprobabilities that the authentication object user will be same person asthe respective enrollees, on the basis of the score and the delta score;and an authentication object user identification function for conductingidentification processing of the authentication object user by comparingthe posterior probabilities with a predetermined threshold A.
 2. Thebiometric authentication system according to claim 1, wherein the priorprobability setting function sets the prior probabilities inclusive of aprior probability that the authentication object user will be anon-enrollee, and the posterior probability calculation functioncalculates the posterior probabilities inclusive of a probability thatthe authentication object user will be a non-enrollee.
 3. The biometricauthentication system according to claim 1, wherein the authenticationobject user identification function determines an enrollee or anon-enrollee having a posterior probability which assumes a maximumvalue among the posterior probabilities exceeding the threshold A to bean identification result.
 4. The biometric authentication systemaccording to claim 1, wherein the authentication object useridentification function determines “unsuccessful authentication” to bean identification result if a posterior probability exceeding thethreshold A does not exist.
 5. The biometric authentication systemaccording to claim 2, wherein when the authentication object user isidentified as a non-enrollee, the authentication object useridentification function determines “impersonation” to be anidentification result, and when whether the authentication object useris an enrollee or a non-enrollee cannot be identified, theauthentication object user identification function determines“unsuccessful identification” to be an identification result.
 6. Thebiometric authentication system according to claim 1, wherein thebiometric information input sensors acquire M pieces of the biometricinformation of the authentication object user, the feature extractionfunction extracts M feature, and the 1:N fast matching function, thedelta score calculation function, the posterior probability calculationfunction and the authentication object user identification functionconduct processing using the M feature.
 7. The biometric authenticationsystem according to claim 5, wherein the biometric information inputsensors acquire one piece of biometric information of the authenticationobject user, the feature extraction function extracts one feature, the1:N fast matching function, the delta score calculation function, theposterior probability calculation function and the authentication objectuser identification function conduct processing using the one feature,and if the authentication object user identification function determines“unsuccessful identification” to be an identification result, then the1:N fast matching function, the delta score calculation function, theposterior probability calculation function and the authentication objectuser identification function repeat the processing on one featureacquired by the biometric information input sensors and extracted by thefeature extraction function.
 8. The biometric authentication systemaccording to claim 1, wherein the 1:N fast matching function rearrangesa matching sequence of the registered templates by referring to thescore table.
 9. The biometric authentication system according to claim1, wherein scores between the registered templates numbering L (L<N) andthe registered templates of other enrollees are recorded in the scoretable.
 10. The biometric authentication system according to claim 1,wherein as for each of the enrollees having found scores, the posteriorprobability calculation function calculates a posterior probability byusing the score and the delta score, and as for each of the enrolleeshaving unfound scores, the posterior probability calculation functioncalculates a posterior probability by using the delta score.
 11. Thebiometric authentication system according to claim 1, wherein as foreach of the enrollees having found scores, the posterior probabilitycalculation function calculates a posterior probability by using thescore, and as for each of the enrollees having unfound scores, theposterior probability calculation function calculates a posteriorprobability by using the delta score.
 12. The biometric authenticationsystem according to claim 8, wherein the 1:N fast matching functionrearranges the sequence of the registered templates to be matched byreferring to the whole or a part of obtained scores.